// Numbas version: exam_results_page_options {"name": "W2a: Solve an equation with a reciprocal-1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variables": {"t": {"group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "name": "t"}, "a": {"group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "name": "a"}, "s2": {"group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "name": "s2"}, "an2": {"group": "Ungrouped variables", "definition": "a*(d-c)", "description": "", "templateType": "anything", "name": "an2"}, "d": {"group": "Ungrouped variables", "definition": "abs(c)+random(2..9)", "description": "", "templateType": "anything", "name": "d"}, "s1": {"group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "name": "s1"}, "b1": {"group": "Ungrouped variables", "definition": "s1*random(1..10)", "description": "", "templateType": "anything", "name": "b1"}, "an1": {"group": "Ungrouped variables", "definition": "t-b*d+b*c", "description": "", "templateType": "anything", "name": "an1"}, "b": {"group": "Ungrouped variables", "definition": "if(a=abs(b1),abs(b1)+2,b1)", "description": "", "templateType": "anything", "name": "b"}, "c": {"group": "Ungrouped variables", "definition": "s2*random(1..9)", "description": "", "templateType": "anything", "name": "c"}}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$

"}, "name": "W2a: Solve an equation with a reciprocal-1", "advice": "

Rearrange the equation by adding {-c} to both sides to get:
\$\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\$
This gives \$\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\$ (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)
and so \$\\simplify{({a} * x + {b}) = {t} / {d -c}}\$ on multiplying both sides by {t}.
Hence \$\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\$
and so \$\\simplify{x={an1}/{an2}}\$ is the solution on dividing both sides by {a}.

", "tags": [], "preamble": {"css": "", "js": ""}, "variable_groups": [], "statement": "\n\t

Solve the following equation for $x$.

\n\t

Input your answer as a fraction or an integer as appropriate and not as a decimal.

\n\t \n\t \n\t \n\t \n\t", "parts": [{"steps": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "\n\t\t\t\t\t

Rearrange the equation by adding {-c} to both sides to get:
\$\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\$

\n\t\t\t\t\t

This gives \$\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\$ (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)

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and so \$\\simplify{({a} * x + {b}) = {t} / {d -c}}\$ on multiplying both sides by {t}.

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Solve this equation for $x$.

\n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t", "useCustomName": false, "scripts": {}, "marks": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "adaptiveMarkingPenalty": 0, "type": "information", "customName": "", "unitTests": []}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"valuegenerators": [], "variableReplacements": [], "scripts": {}, "marks": 3, "checkVariableNames": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.0001, "adaptiveMarkingPenalty": 0, "type": "jme", "unitTests": [], "answer": "{an1}/{an2}", "vsetRangePoints": 5, "showPreview": true, "notallowed": {"showStrings": false, "strings": ["."], "partialCredit": 0, "message": "

Input as a fraction or an integer, not as a decimal.

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\$\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\$

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$x=\\;$ [[0]]

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If you want help in solving the equation, click on \"Show steps\". If you do so then you will lose 1 mark.

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Input all numbers as fractions or integers and not as decimals.

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